If `N_(A)` is Avogadro's number, then the number of oxygen atom in one g-equivalent of oxygen is

Options

A. `N_(A)`
B. `N_(A)//2`
C. `N_(A)//4`
D. `2N_(A)`

Explanation

To find the number of oxygen atoms in one gram equivalent of oxygen, we will follow these steps:

### Step 1: Understand the concept of gram equivalent
A gram equivalent (g-equivalent) is defined as the amount of substance that will react with or replace one mole of hydrogen atoms or one mole of electrons in a reaction. For an element, it can be calculated using the formula:

\[ \text{Gram Equivalent} = \frac{\text{Mass of substance}}{\text{Equivalent weight of substance}} \]

### Step 2: Determine the equivalent weight of oxygen
The equivalent weight of an element can be calculated using the formula:

\[ \text{Equivalent weight} = \frac{\text{Molar mass}}{n} \]

Where:
- Molar mass of oxygen (O) = 16 g/mol
- The n factor for oxygen (in the context of forming O2) is 2 (since one mole of O2 contains two moles of oxygen atoms).

Thus, the equivalent weight of oxygen is:

\[ \text{Equivalent weight of oxygen} = \frac{16 \text{ g/mol}}{2} = 8 \text{ g/equiv} \]

### Step 3: Calculate the mass of oxygen in one gram equivalent
Since we are considering one gram equivalent of oxygen, we have:

\[ \text{Mass of oxygen} = \text{Equivalent weight} = 8 \text{ g} \]

### Step 4: Calculate the number of moles of oxygen
Now, we can calculate the number of moles of oxygen in 8 grams using the formula:

\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{8 \text{ g}}{16 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 5: Calculate the number of oxygen atoms
To find the number of atoms, we use Avogadro's number (N_A), which is approximately \(6.022 \times 10^{23}\) atoms/mol. The number of atoms in 0.5 moles of oxygen is:

\[ \text{Number of atoms} = \text{Number of moles} \times N_A = 0.5 \times N_A = \frac{N_A}{2} \]

### Conclusion
Thus, the number of oxygen atoms in one gram equivalent of oxygen is:

\[ \frac{N_A}{2} \]